Question

Two satellites S1 and S2 revolve around a planet in coplanar circular orbits in the same sense. Their periods of revolution are 1 h and 8 h respectively. The radius of the orbit of S1 is 10^4 km. When S2 is closest to S1,
Find
a) speed of S2 relative to S1 and
b) the angular speed of S2 as observed by an astronaut in S1.
DO NOT GIVE ANY USELESS, FILTHY ANSWERS.​

Answer 1

Hello dear, let's solve this,

Angular speed of satelite s2 w.r.t. s1 when they are closest to each other is given by,

w = |v1-v2| / |r1-r2|

But for planetary motion,

v1 = 2πr1/T1

v2 = 2πr2/T2

w = 2π× |(r1/T1 - r2/T2 ) ÷ (r1-r2)|

w = 2π× |(r1T2 - r2T1)/T1T2| ÷ |r1-r2|

w = 2π× | [r1T2- r2T1] / [T1T2/(r1-r2)] |

This is formula for angular speed of satelite s2 w.r.t. s1.

Hope this was useful...